Extended Adaptive Observer for Linear Systems with Overparametrization

Exponentially stable extended adaptive observer is proposed for a class of linear time-invariant systems with unknown parameters and overparameterization. It allows one to reconstruct unmeasured states and bounded external disturbance produced by a known linear exosystem with unknown initial conditions if a weak requirement of regressor finite excitation is met. In contrast to the existing solutions, the proposed observer reconstructs the original (physical) states of the system rather than the virtual one of its observer canonical form. Simulation results to validate the developed theory are presented.